# Group 333.3 downloaded from the LMFDB on 09 November 2025. 
 
## Various presentations of this group are stored in this file: 
#	 GPC is polycyclic presentation GPerm is permutation group 
#	 GLZ, GLFp, GLZA, GLZq, GLFq if they exist are matrix groups 
 
# Many characteristics of the group are stored as booleans in a record: 
#	 Agroup, Zgroup, abelian, almost_simple,cyclic, metabelian, 
#	 metacyclic, monomial, nilpotent, perfect, quasisimple, rational, 
#	 solvable, supersolvable 
 
# The character table is stored as a record chartbl_n_i where n is the order 
# of the group and i is which group of that order it is. The record is 
# converted to a character table using ConvertToLibraryCharacterTableNC 

 
# Constructions 
GPC := PcGroupCode(4142943486359,333); a := GPC.1; b := GPC.3;
GPerm := Group( (2,17,35,27,10,34,11,13,8)(3,33,32,16,19,30,21,25,15)(4,12,29,5,28,26,31,37,22)(6,7,23,20,9,18,14,24,36), (2,27,11)(3,16,21)(4,5,31)(6,20,14)(7,9,24)(8,35,34)(10,13,17)(12,28,37)(15,32,30)(18,36,23)(19,25,33)(22,29,26), (1,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2) );
GLFp := Group([[[ Z(37)^0, Z(37)^0 ], [ 0*Z(37), Z(37)^0 ]], [[ Z(37)^28, 0*Z(37) ], [ 0*Z(37), Z(37)^12 ]]]);

 
# Booleans 
booleans_333_3 := rec( 
Agroup := true,
Zgroup := true,
abelian := false,
almost_simple := false,
cyclic := false,
metabelian := true,
metacyclic := true,
monomial := true,
nilpotent := false,
perfect := false,
quasisimple := false,
rational := false,
solvable := true,
supersolvable := true); 

 
# Character Table 
chartbl_333_3:=rec(); 
chartbl_333_3.IsFinite:= true; 
chartbl_333_3.UnderlyingCharacteristic:= 0; 
chartbl_333_3.UnderlyingGroup:= GPC;
chartbl_333_3.Size:= 333;
chartbl_333_3.InfoText:= "Character table for group 333.3 downloaded from the LMFDB."; 
chartbl_333_3.Identifier:= " C37:C9 "; 
chartbl_333_3.NrConjugacyClasses:= 13; 
chartbl_333_3.ConjugacyClasses:= [<identity> of ..., f2^2*f3^9, f2*f3^25, f1^2*f2*f3^33, f1*f2*f3^11, f1*f3^8, f1^2*f2^2*f3^32, f1^2*f3^6, f1*f2^2*f3^15, f3, f3^3, f3^2, f3^5];
chartbl_333_3.IdentificationOfConjugacyClasses:= [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13];
chartbl_333_3.ComputedPowerMaps:= [ , [1, 3, 2, 6, 7, 8, 9, 5, 4, 12, 13, 11, 10], [1, 1, 1, 2, 3, 3, 2, 2, 3, 11, 10, 13, 12]];
chartbl_333_3.SizesCentralizers:= [333, 9, 9, 9, 9, 9, 9, 9, 9, 37, 37, 37, 37];
chartbl_333_3.ClassNames:= ["1A", "3A1", "3A-1", "9A1", "9A-1", "9A2", "9A-2", "9A4", "9A-4", "37A1", "37A-1", "37A2", "37A-2"];
chartbl_333_3.OrderClassRepresentatives:= [1, 3, 3, 9, 9, 9, 9, 9, 9, 37, 37, 37, 37];
chartbl_333_3.Irr:= [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, E(3)^-1, E(3)^-1, E(3)^-1, E(3), E(3), E(3), 1, 1, 1, 1], [1, 1, 1, E(3), E(3), E(3), E(3)^-1, E(3)^-1, E(3)^-1, 1, 1, 1, 1], [1, E(9)^-3, E(9)^3, E(9)^4, E(9), E(9)^-2, E(9)^-1, E(9)^-4, E(9)^2, 1, 1, 1, 1], [1, E(9)^3, E(9)^-3, E(9)^-4, E(9)^-1, E(9)^2, E(9), E(9)^4, E(9)^-2, 1, 1, 1, 1], [1, E(9)^-3, E(9)^3, E(9)^-2, E(9)^4, E(9), E(9)^-4, E(9)^2, E(9)^-1, 1, 1, 1, 1], [1, E(9)^3, E(9)^-3, E(9)^2, E(9)^-4, E(9)^-1, E(9)^4, E(9)^-2, E(9), 1, 1, 1, 1], [1, E(9)^-3, E(9)^3, E(9), E(9)^-2, E(9)^4, E(9)^2, E(9)^-1, E(9)^-4, 1, 1, 1, 1], [1, E(9)^3, E(9)^-3, E(9)^-1, E(9)^2, E(9)^-4, E(9)^-2, E(9), E(9)^4, 1, 1, 1, 1], [9, 0, 0, 0, 0, 0, 0, 0, 0, E(37)^2+E(37)^14+E(37)^15+E(37)^18+E(37)^-17+E(37)^-13+E(37)^-8+E(37)^-6+E(37)^-5, E(37)^5+E(37)^6+E(37)^8+E(37)^13+E(37)^17+E(37)^-18+E(37)^-15+E(37)^-14+E(37)^-2, E(37)^3+E(37)^4+E(37)^11+E(37)^-16+E(37)^-12+E(37)^-10+E(37)^-9+E(37)^-7+E(37)^-1, E(37)+E(37)^7+E(37)^9+E(37)^10+E(37)^12+E(37)^16+E(37)^-11+E(37)^-4+E(37)^-3], [9, 0, 0, 0, 0, 0, 0, 0, 0, E(37)^5+E(37)^6+E(37)^8+E(37)^13+E(37)^17+E(37)^-18+E(37)^-15+E(37)^-14+E(37)^-2, E(37)^2+E(37)^14+E(37)^15+E(37)^18+E(37)^-17+E(37)^-13+E(37)^-8+E(37)^-6+E(37)^-5, E(37)+E(37)^7+E(37)^9+E(37)^10+E(37)^12+E(37)^16+E(37)^-11+E(37)^-4+E(37)^-3, E(37)^3+E(37)^4+E(37)^11+E(37)^-16+E(37)^-12+E(37)^-10+E(37)^-9+E(37)^-7+E(37)^-1], [9, 0, 0, 0, 0, 0, 0, 0, 0, E(37)^3+E(37)^4+E(37)^11+E(37)^-16+E(37)^-12+E(37)^-10+E(37)^-9+E(37)^-7+E(37)^-1, E(37)+E(37)^7+E(37)^9+E(37)^10+E(37)^12+E(37)^16+E(37)^-11+E(37)^-4+E(37)^-3, E(37)^5+E(37)^6+E(37)^8+E(37)^13+E(37)^17+E(37)^-18+E(37)^-15+E(37)^-14+E(37)^-2, E(37)^2+E(37)^14+E(37)^15+E(37)^18+E(37)^-17+E(37)^-13+E(37)^-8+E(37)^-6+E(37)^-5], [9, 0, 0, 0, 0, 0, 0, 0, 0, E(37)+E(37)^7+E(37)^9+E(37)^10+E(37)^12+E(37)^16+E(37)^-11+E(37)^-4+E(37)^-3, E(37)^3+E(37)^4+E(37)^11+E(37)^-16+E(37)^-12+E(37)^-10+E(37)^-9+E(37)^-7+E(37)^-1, E(37)^2+E(37)^14+E(37)^15+E(37)^18+E(37)^-17+E(37)^-13+E(37)^-8+E(37)^-6+E(37)^-5, E(37)^5+E(37)^6+E(37)^8+E(37)^13+E(37)^17+E(37)^-18+E(37)^-15+E(37)^-14+E(37)^-2]];
ConvertToLibraryCharacterTableNC(chartbl_333_3);